The confusion lies in the tense of the "when". For giving an action as "when" with a future form, you use present tense.
So a) and c) are correct, but b) makes no sense because the "when" tells me you finished your project in the past, so why are you making a future promise? :)
For the second question, simply use "when (or after) I finish my project, I will let you know". Again, the main action of the sentence is letting your friend know, and finishing it can be in present tense to represent "when".
Alternately, use "I'll finish my project, then (I'll) let you know."